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Lecture 14 Neutrino-Powered Explosions Mixing, Rotation, and Making Black Holes Baade and Zwicky, Proceedings of the National Academy of Sciences, (1934) “With all reserve we advance the view that a supernova represents the transition of an ordinary star into a neutron star consisting mainly of neutrons. Such a star may possess a very small radius and an extremely high density. As neutrons can be packed much more closely than ordinary nuclei and electrons, the gravitational packing energy in a cold neutron star may become very large, and under certain conditions, may far exceed the ordinary nuclear packing fractions ...” Chadwick discovered the neutron in 1932 though the idea of a neutral massive particle had been around since Rutherford, 1920. For the next 30 years little progress was made though there were speculations: Hoyle (1946) - supernovae are due to a rotational bounce!! Hoyle and Fowler (1960) – Type I supernovae are due to the explosions of white dwarf stars Fowler and Hoyle (1964) – other supernovae are due to thermonuclear burning in massive stars – aided by rotation and magnetic fields The explosion is mediated by neutrino energy transport .... Colgate and White, (1966), ApJ, 143, 626 see also Arnett, (1966), Canadian J Phys, 44, 2553 Wilson, (1971), ApJ, 163, 209 But there were fundamental problems in the 1960’s and early 1970’s that precluded a physically complete description • Lack of realistic progenitor models (addressed in the 80s) • Neglect of weak neutral currents – discovered 1974 • Uncertainty in the equation of state at super-nuclear densities (started to be addressed in the 80s) • Inability to do realistic multi-dimensional models (still in progress) • Missing fundamental physics (still discussed) BBAL 1979 • The explosion was low entropy • Heat capacity of excited states kept temperature low • Collapse continues to nuclear density and beyond • Bounce on the nuclear repulsive force • Possible strong hydrodynamic explosion • Entropy an important concept What is the neutrino emission of a young neutron star? Time-integrated spectra Woosley, Wilson, & Mayle (1984, 1986) see also Bisnovatyi Kogan et al (1984) *Krauss, Glashow and Schramm (1984) Typical values for supernovae; electron antineutrinos only Cosmological Neutrino Flux Ando, 2004, ApJ, 607, 20 Wilson 20 M-sun Myra and Burrows, (1990), ApJ, 364, 222 Neutrino luminosities of order 1052.5 are maintained for several seconds after an initial burst from shock break out. At late times the luminosities in each flavor are comparable though the - and neutrinos are hotter than the electron neutrinos. Woosley et al. (1994), ApJ,, 433, 229 K II 2140 tons H2O IMB 6400 tons “ Cerenkov radiation from n(p,n)e+ - dominates n(e-,e-)n - relativistic e all flavors n less than solar neutrino flux but neutrinos more energetic individually. Neutrino Burst Properties: E tot 3 GM 2 ~ 5 R ~ 3 1053 erg M = 1.5 M R = 10 km emitted roughly equally in n e , n e , n , n , n , and n Time scale R2 1 Diff ~ l n l c n ~1016 cm 2 gm -1 for n 50 MeV (next page) ~ 3 1014 gm cm -3 Diff l ~ 30 cm (2 106 ) 2 ~ ~ 5 sec 10 30 3 10 R ~ 20 km Very approximate At densities above nuclear, the coherent scattering cross section (see last lecture) is no longer appropriate. One instead has scattering and absorption on individual neutrons and protons. 2 Scattering: n s 1.0 10 20 En 2 -1 cm gm MeV Absorption: n a 4 n s The actual neutrino energy needs to be obtained from a simulation but is at least tens of MeV. Take 50 MeV for the example here. Then n ~1016 cm 2 g -1. Gives lmfp : 1 m and diff : few seconds. Temperature: Etot Ln 1052 erg s-1 per flavor 6 Diff 7 2 4 4 R T n n 16 Tn 4.5 MeV for R 20 km and n 3 sec Actually Rn is a little bit smaller and Diff is a little bit longer but 4.5 MeV is about right. * * See also conference proceedings by Wilson (1982) 20 Solar Masses Mayle and Wilson (1988) bounce = 5.5 x 1014 g cm-3 Explosion energy at 3.6 s 3 x 1050 erg Mayle and Wilson (1988) Herant and Woosley, 1995. 15 solar mass star. successful explosion. (see also Herant, Benz, & Colgate (1992), ApJ, 395, 642) Energy deposition here drives convection Bethe, (1990), RMP, 62, 801 Velocity Neutrinosphere (see also Burrows, Arnett, Wilson, Epstein, ...) gain radius radius 3000 km s 1 Infall n Accretion Shock Inside the shock, matter is in approximate hydrostatic equilibrium. Inside the gain radius there is net energy loss to neutrinos. Outside there is net energy gain from neutrino deposition. At any one time there is about 0.1 solar masses in the gain region absorbing a few percent of the neutrino luminosity. Burrows (2005) 8.8-Solar mass Progenitor of Nomoto: Neutrino-driven Wind Explosion Burrows et al , 2007, AIPC, 937, 370 Explosion energy 10 50 erg QuickTime™ and a YUV420 codec decompressor are needed to see this picture. Burrows, Hayes, and Fryxell, (1995), ApJ, 450, 830 QuickTime™ and a YUV420 codec decompressor are needed to see this picture. 15 Solar masses – exploded with an energy of order 1051 erg. see also Janka and Mueller, (1996), A&A, 306, 167 QuickTime™ and a YUV420 codec decompressor are needed to see this picture. At 408 ms, KE = 0.42 foe, stored dissociation energy is 0.38 foe, and the total explosion energy is still growing at 4.4 foe/s Mezzacappa et al. (1998), ApJ, 495, 911. QuickTime™ and a YUV420 codec decompressor are needed to see this picture. Using 15 solar mass progenitor WW95. Run for 500 ms. 1D flux limited multi-group neutrino transport coupled to 2D hydro. No explosion. QuickTime™ and a YUV420 codec decompressor are needed to see this picture. QuickTime™ and a Video decompressor are needed to see this picture. Beneficial Aspects of Convection • Increased luminosity from beneath the neutrinosphere • Cooling of the gain radius and increased neutrino absorption • Transport of energy to regions far from the neutrinosphere (i.e., to where the shock is) Also Helpful • Decline in the accretion rate and accompanying ram pressure as time passes • A shock that stalls at a large radius • Accretion sustaining a high neutrino luminosity as time passes (able to continue at some angles in multi-D calculations even as the explosion develops). Scheck et al. (2004) Challenges • Tough physics – nuclear EOS, neutrino opacities • Tough problem computationally – must be 3D (convection is important). 6 flavors of neutrinos out of thermal equilibrium (thick to thin region crucial). Must be follwoed with multi-energy group and multi-angles • Magnetic fields and rotation may be important • If a black hole forms, problem must be done using relativistic (magnto-)hydrodynamics (general relativity, special relativity, magnetohydrodynamics) When Massive Stars Die, How Do They Explode? Neutron Star + Neutrinos Colgate and White (1966) Arnett Wilson Bethe Janka Herant Burrows Fryer Mezzacappa etc. 10 Neutron Star + Rotation Hoyle (1946) Fowler and Hoyle (1964) LeBlanc and Wilson (1970) Ostriker and Gunn (1971) Bisnovatyi-Kogan (1971) Meier Wheeler Usov Thompson etc 20 Black Hole + Rotation Bodenheimer and Woosley (1983) Woosley (1993) MacFadyen and Woosley (1999) Narayan (2004) All of the above? 35 M The answer depends on the mass of the core of helium and heavy elements when the star dies and on its angular momentum distribution. Rotationally Powered Models Common theme: Need iron core rotation at death to correspond to a pulsar of < 5 ms period if rotation and B-fields are to matter. This is much faster than observed in common pulsars. A concern: If calculate the presupernova evolution with the same efficient magnetic field generating algorithms as used in some core collapse simulations, will it be rotating at all? Field would up until magnetic pressure exceeds ram pressure. Explosion along poles first. Maybe important even in other SN mechanisms during fall back Burrows et al 2007, ApJ, 664, 416 Assuming the emission of high amplitude ultra-relativistic MHD waves, one has a radiated power P ~ 6 x 1049 (1 ms/P) 4 (B/1015 gauss) 2 erg s -1 and a total rotational kinetic energy E rot ~ 4 x 1052 (1 ms/P) 2 (10 km/R) 2 erg For magnetic fields to matter one thus needs magnetar-like magnetic fields and rotation periods (for the cold neutron star) of < 5 ms. This is inconsistent with what is seen in common pulsars. Where did the energy go? Magnetic torques as described by Spruit, A&A, 381, 923, (2002) Aside: Note an interesting trend. Bigger stars are harder to explode using neutrinos because they are more tightly bound and have big iron cores. But they also rotate faster when they die. Mixing During the Explosion The Reverse Shock and Rayleigh-Taylor Instability: The Sedov solution (adiabatic blast wave) For Ar - vshock A 1 5 E 1 5 t 3 / 5 3 vshock constant < 3 vshock slows down > 3 vshock speeds up 5 1 2 n 2 Et RS A n dimension of space const = f(n ) Korobeinikov (1961) If r 3 increases with radius, the shock will slow down. The information that slowing is occuring will propagate inwards as a decelerating force directed towards the center. This force is in the opposite direction to the density gradient, since the density, even after the explosion, generally decreases for the material farther out. Rayleigh-Taylor instability and mixing Example: For constant density and an adiabatic blast wave. The constants of the problem are Einitial and . We seek a solution r (t , Einitial , ). Assume that these are the only variables to which r is sensitive. Units E E gm cm 2 sec 2 gm cm3 cm5 E 2 5 r t 2 sec 1/ 5 E r K initial t 2 / 5 1/ 5 dr 2 Einitial 3/ 5 v K which is our =0 case t dt 5 25 solar mass supernova, 1.2 x 1051 erg explosion 2D Shock log RT-mixing Calculation using modified FLASH code – Zingale & Woosley Diagnosing an explosion Kifonidis et al. (2001), ApJL, 531, 123 Left - Cas-A SNR as seen by the Chandra Observatory Aug. 19, 1999 The red material on the left outer edge is enriched in iron. The greenish-white region is enriched in silicon. Why are elements made in the middle on the outside? Right - 2D simulation of explosion and mixing in a massive star - Kifonidis et al, Max Planck Institut fuer Astrophysik Joggerst et al, 2009 in prep for ApJ. Z = 0 and 10(-4) solar metallicty RSG BSG Remnant masses for Z = 0 supernovae of differing masses and explosion energies Zhang, Woosley, and Heger (2008) `` See Zhang et al for other tables with, e.g., different maximum neutron star masses Thorsett and Chakrabarty, (1999), ApJ, 512, 288 If in the models the mass cut is taken at the edge of the iron core the average gravitational mass for for stars in the 10 – 21 solar mass range is (12 models; above this black holes start to form by fall back): 1.38 0.16 M Ransom et al., Science, 307, 892, (2005) find compelling evidence for a 1.68 solar mass neutron star in Terzian 5 If one instead uses the S = 4 criterion, the average from 10 – 21 solar masses is 1.45 0.18M From 10 to 27 solar masses the average is Vertical line is at 1.35 0.04 M 1.53 0.22 M Caveats: Binary membership Minimum mass neutron star Small number statistics Prompt Black Hole Formation? Woosley and Weaver (1995) Fryer, ApJ, 522, 413, (1999) Fryer (1999) 100 Solar Masses Woosley, Mayle, Wilson, and Weaver (1985)